The position of a particle moving along the x axis is given in centimeters by x

Question

The position of a particle moving along the x axis is given in centimeters by x = 9.44 + 1.89 t3, where t is in seconds. Calculate (a) the average velocity (in cm/s) during the time interval t = 2.00 s to t = 3.00 s; (b) the instantaneous velocity at t = 2.00 s; (c) the instantaneous velocity at t = 3.00 s; (d) the instantaneous velocity at t = 2.50 s; and (e) the instantaneous velocity when the particle is midway between its positions at t = 2.00 s and t = 3.00 s. Give all answers in cm/s. (Please if possible, show work and label your answers a) b) etc.)

Explanation / Answer

total displacement btw 2 & 3 sec = 9.44 + 1.89*33 - (9.44 + 1.89*23) = 35.91

(a)average velocity = 35.91/1 =35.91 cm/sec

(b)Velocity function = 1.89*3 t2

velocity at t=2 sec = 32.12 cm / sec

(c) =1.89*3*32 = 51.03cm/sec

(d) = 1.89*3*2.52 = 22.68 cm/sec

(e) position at t=2 sec = 24.56 cm

position at t=3sec = 60.47 cm

midway position = (60.47+24.56)/2 = 42.515 cm

t when x= 42.515

42.515 = 9.44 + 1.89 * t3

t~ 2.6 sec

velocity at t~2.6 sec = 1.89*3* 2.62 =38.3292 cm /sec

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